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                                                                    EXHIBIT 4(z)

AMENDING AGREEMENT TO EXHIBIT "B" OF THE MASTER AGREEMENT TO SUPPLY LOCAL
INTERCONNECTION SERVICES DATED FEBRUARY THE 25TH OF 1999 (HEREINAFTER THE
"AMENDING AGREEMENT"), EXECUTED, ON ONE PART, BY MAXCOM TELECOMUNICACIONES, S.A.
DE C.V. (HEREINAFTER "MAXCOM"), HEREBY REPRESENTED BY MR. ROGELIO ESPINOSA
CANTELLANO, AND ON THE OTHER PART, BY TELEFONOS DE MEXICO, S.A. DE C.V.
(HEREINAFTER "TELMEX"), HEREBY REPRESENTED BY MR. SERGIO RODRIGUEZ MOLLEDA,
REGARDING THE INTERCONNECTION OF THEIR RESPECTIVE FIXED LOCAL SERVICE NETWORKS.

                                 REPRESENTATIONS

BOTH PARTIES REPRESENT:

a)    That on February the 25th of 1999, they executed the Local Interconnection
      Services Supply Master Agreement regarding the interconnection of their
      respective Fixed Local Service Networks (hereinafter the "Agreement").

b)    That this Amending Agreement shall become an integral part of the
      Agreement executed by and between Telmex and Maxcom.

c)    That they desire to amend Exhibit "B" to the Agreement the parties hereto
      executed on February the 25th of 1999, under the terms set forth in this
      Amending Agreement, pursuant to the following:

                                     CLAUSE

SOLE CLAUSE.

            Both parties hereto agree to amend Exhibit "B" to the Local
Maxcom-TELMEX Local Interconnection Master Agreement in its entirety, to read as
follows:

                                   EXHIBIT "B"

OFFSETTING AGREEMENT OF LOCAL INTERCONNECTION SWITCHING SERVICES EXECUTED, ON
ONE PART, BY TELEFONOS DE MEXICO, S.A. DE C.V. (HEREINAFTER "TELMEX"), HEREBY
REPRESENTED BY MR. SERGIO RODRIGUEZ MOLLEDA, AND ON THE OTHER PART, BY MAXCOM
TELECOMUNICACIONES, S.A. DE C.V. (HEREINAFTER "MAXCOM"), HEREBY REPRESENTED BY
ROGELIO ESPINOSA CANTELLANO, PURSUANT TO THE FOLLOWING REPRESENTATIONS AND
CLAUSES:

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                                 REPRESENTATIONS

BOTH PARTIES REPRESENT:

a)    That they execute this Offsetting Agreement derived from the Local
      Interconnection Services Supply Master Agreement (hereinafter the "Local
      Interconnection Agreement") executed by and between MAXCOM and TELMEX on
      this same date.

b)    That they agree to incorporate herein by reference in this Offsetting
      Agreement the Representations of the Local Interconnection Agreement,
      without the need to transcribe them.

c)    That they desire to execute this Offsetting Agreement in order to offset
      between each of them the considerations derived from the reciprocal supply
      of the Local Interconnection Switching Services, provided however such
      considerations fall within the scope determined by the unbalance
      thresholds set forth in this Offsetting Agreement, according to the
      mechanisms described herein, and thus agree that this Offsetting Agreement
      shall be governed by the foregoing Representations and by the following:

                                     CLAUSES

            FIRST CLAUSE. PURPOSE. The parties agree to execute this Offsetting
Agreement in order to offset between each of them the considerations derived
from the reciprocal supply of Local Interconnection Switching Services, provided
however such considerations fall within the scope determined by the unbalance
thresholds set forth in this Offsetting Agreement, and pursuant to the following
terms and conditions.

            SECOND CLAUSE. UNBALANCE. The monthly unbalance shall be estimated
according to the following formula (hereinafter the "Unbalance"):

* If MAXCOM's CP is greater than TELMEX's CP, the following shall apply:

((MAXCOM's CP - TELMEX's CP)/(MAXCOM's CP + TELMEX's CP)) x 100%.

* If TELMEX's CP is greater than MAXCOM's CP, the following shall apply:

((TELMEX's CP - MAXCOM's CP)/(MAXCOM's CP + TELMEX's CP)) x 100%.

WHERE:

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             MAXCOM's CP=   Is the amount that results from multiplying the
                            total sum of minutes of the Local Interconnection
                            Switching Services supplied by TELMEX to MAXCOM
                            during the month in question times the rate agreed
                            by the parties in Exhibit "A" to the Local
                            Interconnection Agreement.

             TELMEX's CP=   Is the amount that results from multiplying the
                            total sum of minutes of the Local Interconnection
                            Switching Services supplied by MAXCOM to TELMEX
                            during the month in question times the rate agreed
                            by the parties in Exhibit "A" to the Local
                            Interconnection Agreement.

TELMEX shall not include the following traffic in the estimate of the unbalance:

a.    The traffic originated in MAXCOM's numbers that correspond to Customers'
      Attention Center, commonly named "Call Centers.

b.    The traffic generated by customers allocated to the new series that MAXCOM
      put into service. A new series shall be the one that starts to be used for
      to the generation of the Local traffic of MAXCOM's users, subsequent to
      the date when this document is executed.

c.    The traffic generated by MAXCOM's new customers who have one or more links
      (E1).

The exceptions indicated in the foregoing subparagraphs shall apply, provided
however, the result of the unbalance obtained does not go against Telmex, in
which case the parties shall make the adjustments required to maintain the
unbalance below the threshold agreed upon.

In case any of the events in preceding subparagraphs (b) and (c) takes place,
TELMEX shall not take into account the pertinent traffic during the following
180 days, counted as of the date when MAXCOM gives written notice of the
existence of such event to estimate the unbalance. It shall be understood that
the changes of phone number or firm name are not deemed as new customers.

            THIRD CLAUSE. OFFSETTING. During each invoicing period, the parties
hereto bind to offset to each other the considerations that they may owe each
other due to the Local Interconnection Switching Services in a reciprocal and
symmetric manner, provided however there is an Unbalance that exceeds the
threshold of 18% (eighteen percent) which equals considerations of 59% and 41%.
As of January the 1st of 2005, and in the future, until the parties execute a
new Amending Agreement to Exhibit "B", the unbalance threshold shall be of 15%
(fifteen percent) which equals considerations of 57.5% and 42.5%, and shall be
applied

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during the life of the Local Interconnection Master Agreement executed
by and between MAXCOM and TELMEX, and of this Offsetting Agreement.

For purposes of this Offsetting Agreement and of the Local Interconnection
Master Agreement executed by and between MAXCOM and TELMEX, the parties agree
that the offsetting shall be understood as the discharge of debts between the
parties derived from the reciprocal supply of the Local Interconnection
Switching Services, provided however the Unbalance falls within the threshold in
question.

Both parties agree that the aforesaid threshold shall be reviewed as of
September the 1st of 2005, according to the behavior of traffic from the period
that starts as of the date when the Local Interconnection Master Agreement
executed by and between MAXCOM and TELMEX becomes effective.

            FOURTH CLAUSE. PAYMENT OF CONSIDERATIONS DUE TO THE UNBALANCE.

The parties agree that they shall not pay to each other any consideration
whenever the Unbalance is no greater than the threshold mentioned in the third
clause of this Offsetting Agreement.

The Parties agree that in case the Unbalance is greater than the thresholds set
forth in the preceding Third Clause, the parties shall be bound to pay the
considerations under their care for the pertinent period in full, without any
offsetting. The purpose of this last provision is to discourage undue practices
in Interconnection matters, as well as practices that tend to obtain unjustified
advantages from this Offsetting Agreement.

The parties agree that in case they would be bound to pay either chargeable to,
or in favor of, any of the parties under the terms hereunder, they shall be
subject to the terms, conditions and rates specified in the Fourth Clause of the
Local Interconnection Agreement and the Exhibit "A" thereto.

            FIFTH CLAUSE. OFFSETTING DUE TO CALLS MADE TO INTERNET SERVICE
PROVIDERS. Both parties agree that all the calls originated in any of the
networks which destination is an Internet Service Provider, they shall offset
the considerations derived in 100% (one hundred percent), this is, both TELMEX
and MAXCOM release each other from any obligation to pay the other party that
results due to the traffic of calls indicated in this paragraph. Therefore, the
parties agree that the traffic of interconnection that corresponds to the calls
destined to an Internet Service Provider shall not be included in order to
estimate the Unbalance indicated in the second clause hereunder.

Likewise, both parties bind themselves to inform to the other party the phone
numbers contracted with an Internet Service Provider and, in case any of the
parties becomes aware that any of these phone numbers have not been informed, it
shall

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immediately proceed to make the pertinent processes so that these numbers become
part of the offsetting described in the above clauses hereunder. The party to
whom such phone numbers are allocated contracted by an Internet Service Provider
shall register such phone numbers in its invoicing system within 5 (five)
business days following the date when the other party informs of such event, at
the latest.

            SIXTH CLAUSE. MECHANISMS FOR AUDITING AND MONITORING. PENALTIES. In
order to prevent, detect and avoid fraudulent practices in interconnection
matters, the parties hereto shall observe the terms and conditions agreed upon
in Exhibit 18.11 to the Local Interconnection Agreement executed by and between
MAXCOM and TELMEX; this mechanism shall also apply for purposes of the
provisions of the Eleventh Clause hereunder.

            SEVENTH CLAUSE. GROUNDS TO SUBSTITUTE THE OFFSETTING AGREEMENT.
Notwithstanding the provisions of the sixth clause hereunder, or the provisions
of the Local Interconnection Agreement, the parties agree that this Offsetting
Agreement shall be substituted with Exhibit "B bis", in case any of the
following actions in the exchange of traffic under this Offsetting Agreement
take place:

a)    The change of number of origin.

b)    The alteration to the type of traffic (converting National Long Distance,
      International Long Distance of Mobile Local Traffic into Fixed Local
      Traffic).

c)    The delivery of the traffic generated by other operator, and whenever such
      traffic has not been carried using the Local Transit Services foreseen in
      the Local Interconnection Agreement.

d)    The traffic originated by any of the parties in a Group of Local Service
      Exchanges different to the exchanges where said traffic is delivered.

In order to make such substitution, the parties agree to previously observe the
procedure set forth in the nineteenth clause of the Local Interconnection
Service Agreement.

            EIGHTH CLAUSE. LONG DURATION CALLS. In case the Unbalance for any
monthly period exceeds 18% (eighteen percent), or 15% (fifteen percent) of the
unbalance thresholds, as the case may be, as set forth in the Third Clause
hereunder, the parties agree to carry out the following:

8.1 The duration of all the calls included in the monthly period in which the
Unbalance exceeded 18% (eighteen percent) or 15% (fifteen percent), as
applicable, shall be analyzed.

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8.2 The percentage of calls which duration is equal or greater to 5 (five)
minutes shall be determined.

8.3 In case the percentage of calls indicated in subparagraph 8.2 exceeds 20%
(twenty percent) of the total amount of the calls included in the pertinent
monthly period, the parties agree to offset 100% (one hundred percent) of the
amount of minutes that correspond to the calls that exceed the aforesaid 20%
(twenty percent). To carry out the cited offsetting, the average of minutes of
the Long Duration calls must be obtained, and the result shall be multiplied
times the number of calls that exceed 20%. The offsetting indicated in this
subparagraph shall be carried out, provided however it is proven that these
calls are local calls.

8.4 In case the percentage of calls indicated in subparagraph 8.2 is lower or
equal to 20% (twenty percent) of the total calls included in the pertinent
monthly period, the parties shall pay the considerations according to the
contents of the fourth clause hereunder.

8.5 In case the event foreseen in subparagraph 8.3 takes place, the parties
shall estimate again the Unbalance for the pertinent monthly period in
accordance to the provisions of the second clause hereunder, without including
the minutes that correspond to the calls that exceed 20% (twenty percent)
indicated in subparagraph 8.3.

8.6 If, subsequently to the recalculation of the Unbalance made according to the
provisions of subparagraph 8.5 above, the percentage of the Unbalance for the
pertinent monthly period continues to exceed 20% (twenty percent), the parties
shall pay the considerations according to the provisions set forth of the fourth
clause hereunder.

            NINTH CLAUSE. LIFE OF THE AGREEMENT. The parties agree that this
Offsetting Agreement shall become effective as of the date of its execution, and
shall remain in force as long as the Local Interconnection Agreement remains
effective. To renew it, the terms and conditions of subparagraph 16.2 of the
Local Interconnection Agreement shall be observed.

            TENTH CLAUSE. TREATMENT AS MOST FAVORED NATION. Notwithstanding any
provision to the contrary set forth in this Exhibit, the Parties agree that in
case that (i) derived from any agreement or out-of-court settlement executed by
TELMEX with any third party, TELMEX grants to said third party an Unbalance
threshold greater to 18% (eighteen percent) until December the 31st of 2004, and
greater to 15% (fifteen percent) as of January the 1st of 2005, and
subsequently, and until a new agreement is executed in such regard between the
parties, or (ii) if a third party obtains from TELMEX an Unbalance threshold
greater to 18% (eighteen percent) up to December the 31st of 2004, and greater
to 15% (fifteen percent) as of January the 1st of 2005 and subsequently, and
until a new agreement is executed in such regard between the parties derived
from an order or

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a judicial decision that becomes final and unappealable rendered in any
instance, or derived from a decision or administrative act that becomes final
and unappealable, rendered by any governmental authority voluntarily or to
comply with an order or judicial decision that becomes final and unappealable,
rendered in any instance, then the Unbalance threshold indicated hereunder shall
be adjusted to reflect the result of granting MAXCOM the benefits that TELMEX
would have granted to the third party in question, as result of the
materialization of any of the events set forth under subparagraphs (i) and (ii)
of this Clause. TELMEX shall grant MAXCOM the same benefits that it would have
granted to such third party, starting from the moment when, derived from any
agreement or out-of-court settlement executed by TELMEX with any third party,
TELMEX grants to such third party an Unbalance threshold greater to the
threshold agreed hereunder with MAXCOM or, from the moment when, derived from an
order or judicial decision that becomes final and unappealable, rendered in any
instance or derived from a decision or administrative act that becomes final and
unappealable rendered by any governmental authority, voluntarily or to comply
with an order or judicial decision that becomes final and unappealable, rendered
in any instance, a third party obtains from TELMEX an Unbalance threshold
greater to the threshold agreed herein with MAXCOM.

            ELEVENTH CLAUSE.- TERMINATION OF INTERNATIONAL TRAFFIC.

            In case TELMEX verifies, once the mechanism described in the Sixth
Clause hereunder is followed, that MAXCOM, directly and due to causes
attributable to Maxcom or to a third party, acting with Maxcom's assistance,
carries out the Termination of International Traffic in Offsetting Agreements,
TELMEX shall be entitled to collect the following from MAXCOM:

      (i)   The amount that results from multiplying the 2004 Interconnection
            Rate (agreed in Number 1 of the First Clause hereunder) times the
            number of minutes of Termination of International Traffic in
            Offsetting Agreements, plus the amounts expressed in the following
            subparagraph.

      (ii)  The amount that results from multiplying the rate of the Second
            Payment of the Updated Basis Rate, this is, USD$0.0053 (fifty-three
            ten-thousandth of dollar of the United States of America) times the
            number of minutes of Termination of International Traffic in
            Offsetting Agreements or any other rate agreed upon by the parties
            for such purpose, either hereunder or in other agreements, whichever
            is lesser.

In case the direct liability of MAXCOM in handling the traffic indicated in this
Clause is proven, the minutes of traffic shall not be counted in order to
estimate the unbalance.

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            TWELFTH CLAUSE. CONTRACTUAL ACKNOWLEDGMENT.- This Amending Agreement
represents the full, entire and sole expression of the decision taken by TELMEX
and MAXCOM, and thus any accord, agreement, covenant, document, notice or offer
made prior to this Amending Agreement, whether verbal or written, and which
relates directly or indirectly to the subject matter of this instrument, shall
become henceforth null and void.

            THIRTEENTH CLAUSE. JURISDICTION. The parties hereto agree that in
case of a dispute regarding the construction or performance of this Offsetting
Agreement, said dispute shall be settled pursuant to the provisions of the
Nineteenth Clause of the Local Interconnection Agreement signed by the parties.

            The representatives of the parties, duly authorized, signed this
Exhibit in three counterparts in Mexico City, Federal District, on August the
5th of 2004.

           TELEFONOS DE MEXICO,                 MAXCOM TELECOMUNICACIONES,
               S.A. DE C.V.                             S.A. DE C.V.

                 (Signed)                               (Signed)
   ----------------------------------      ----------------------------------
      By: Sergio Rodriguez Molleda            By: Rogelio Espinosa Cantellano
         Legal Representative.                     Legal Representative.

                WITNESS                                 WITNESS

         (Illegible signature)                    (Illegible signature)
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